In the operation of an optical element such as a Mach-Zehnder modulator, there is a need to adjust the difference in phase of propagating light between arms in two optical waveguides (called arms) constituting a Mach-Zehnder interferometer to a desired value with improved efficiency and with improved controllability by means of a direct-current voltage. Forward bias voltages are supplied to pin diodes formed in the optical waveguides to inject electron and hole carriers into an optical waveguide core, thereby enabling such phase adjustment to be performed with efficiency. Structures including rib waveguides or side grating waveguides, for example, have been disclosed as structures for such phase modulators using pin diodes. An art relating to a structure including side grating waveguides is disclosed in Non-Patent Document 1: S. Akiyama et al., “Compact PIN-Diode-Based Silicon Modulator Using Side-Wall-Grating Waveguide,” IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 19, NO. 6, pp. 3401611-3401611, 2013.
In a phase modulator having side grating waveguides, an optical waveguide core is undoped, one of the side grating waveguides in the form of fins is doped with a p-type impurity, and the other of the side grating waveguides is doped with an n-type impurity, thereby forming pin diodes. Voltages are applied in forward directions to the diodes to inject electrons and holes into the optical waveguide core through the side grating waveguides, thereby changing the phase of propagating light. In such phase adjustment, there is a need to adjust stepwise the phase of propagating light ordinarily from 0 to π with a sufficiently small pitch. The phase modulator having the side grating waveguides is capable of changing the phase of propagating light in such a way by continuously changing voltages supplied to electrodes of the phase modulator.
The conventional diode-type phase modulator using forward bias voltages has the advantage of having a high efficiency of phase change with respect to a voltage input per unit length of the phase modulator.
FIG. 7 is a characteristic diagram illustrating voltage dependences of phase change (FIG. 7A) and current (FIG. 7B) in the conventional phase modulator having side grating waveguides. With a short operating length of about 250 μm, changes in phase from 0 to π are obtained by changing voltages supplied to the phase modulator from 0 to 1 V in the forward direction with respect to the diodes.
On the other hand, there is a demand for changing the phase of propagating light stepwise in a simple and convenient way with improved controllability even in a high-speed multivalue modulator. Device structures each having, for this purpose, a plurality of phase modulators with separate electrodes connected one after another along an optical axis are disclosed in Patent Document 1: International Publication Pamphlet No. WO2011/043079, and Non-Patent Document 2: X. Wu et al., “A 20 Gb/s NRZ/PAM-4 1V transmitter in 40 nm CMOS driving a Si-photonic modulator in 0.13 μm CMOS” in 2013 IEEE International Solid-State Circuits Conference Digest of Technical Papers, Proceedings, pp. 128-129. In this type of device structure, voltages supplied to divided small phase modulators are binary on-off signals, and the phase change in the entire element is modulated stepwise according to the number of small phase modulators turned on.
The pin diode phase adjustment method conventionally used is thought to ensure an improved efficiency but entails a difficulty in performing phase control with high accuracy and stability for phase adjustment. As indicated in FIG. 7, the phase is exponentially changed by a range of voltage about 0.6 to 0.8 V in which the diode is turned on. Also, the gradient of phase change with respect to the voltage after the diode is turned on is considerably steep and the phase is changed largely by a small change in voltage. Adjusting the phase stepwise to the desired value with respect to such a nonlinear function requires correctly grasping the function in advance and applying a voltage to the pin diode such as to compensate for the change. The circuit for voltage control is therefore made complicated, which leads to an increase in cost. Further, even in a case where such control is performed, it is necessary to control stepwise the voltage to be supplied to the diode with an accuracy of 0.1 V or less in order to perform phase adjustment stepwise with accuracy. In general, it is difficult to control with an accuracy of about 0.1 V a voltage generated in an electronic circuit having a CMOS transistor or the like, and sufficient controllability is not obtained in the case of such control. Thus, the challenge to the conventional phase adjustment method using pin diodes is to perform control in a simple and convenient way with improved controllability.
In the case of the device structures disclosed in Patent Document 1 and Non-Patent Document 2, voltages supplied to divided small phase modulators are binary on-off signals, as described above, and there is no need to set stepwise the voltages to be supplied to the phase modulators. Therefore, stepped phase changes can be made with a drive circuit in a simple and convenient way. In these related arts, however, phase modulators of a multiple quantum well structure or the like to be used with MOS capacitances and inverse bias voltages, which are suitable for high-speed modulation but are low in phase modulation efficiency, are used. The challenge to these related arts is to increase the phase modulation efficiency. Also, these phase modulators have no such nonlinearity in phase change, as that of pn diodes, and no description has been made of any method for causing a certain phase change in a simple and convenient way with improved controllability in divided individual small phase modulators when a nonlinearity such as that of diodes exists.